No, nothing gets terminated automatically. Mega_Septile is right I think:
I think that the reason you can't find the five year old user is (I'm assuming) there can only be a limited number of user pages, and when a new user joins, the last user on the last page gets bumped back into the void where they cannot be seen.
There is a bit of a quirk in the the user lists where the final page of nagivation is stuck on #334, and it's impossible to view users past that point. So the older users were pushed to a hypothetical 335th page (and so on), which doesn't exist and that's why you can't see them. I tested, and modifying the URL manually doesn't change this.
This has existed for a really long time which is why I eventually noticed it. If you want proof that the users beyond page 334 exist: each page of users has 60 users listed. If there are 334 pages, that makes 20,040 users. The stats panel on the side of the site says we nearly triple that number. So the number has likely been stuck for years.
I think the user pages just terminate after the 20,000th user, and since page 335 would start with a user ranked above that number, it won't display. Pokemaster might know why this is.
